Decoupled joint inversion with variable splitting: example scheme for magnetotelluric, seismic and gravity data

We present a general framework for multiphysics joint inversion of any number of geophysical data sets. Its main feature is the use of the variable splitting approach: an auxiliary multiparameter model space is introduced in which minimization of the coupling and stabilizing functionals is carried out. The use of rediscretization and interpolation to map between this auxiliary space and the model spaces allows the coupled models to have completely different parametrizations. Joint inversion is decoupled into the individual inversion and the coupling-regularization subproblems, each of which can be solved by a different optimization algorithm. For each subproblem, the linking term controlling the distance between the model and the corresponding auxiliary variable takes the form of a quadratic regularization with a reference model. As a result, any existing inversion code supporting such regularization can be integrated without modifications into the developed framework. As a concrete example scheme, we consider an application of the framework to 3-D joint inversion of magnetotelluric, seismic refraction and gravity data. We discuss different coupling functionals, mainly those corresponding to the more universal structural constraints: joint total variation, joint minimum support, cross-gradient, one-way cross-gradient and their combinations for a general multimodel case. The use of coupling based on explicit 'petrophysical' relationship between the properties is also considered. Performance of the developed framework is studied on three synthetic cases: a time-lapse joint inversion of full-tensor gravity gradiometry and seismic data, a joint inversion of magnetotelluric, seismic and gravity data and a joint inversion for electrical resistivity tomography and audio-magnetotellurics.